Customizing Move Hotkey
i think you have to remove every other keybinding to "M" so there are no conflicts.

For me,   

3dview -> object mode-> move to collection is blocking

but I would advise you to use "G" for G.rab as it is, because it's not Move - it is grab. You grab stuff in all Editor windows and then you move it around… Keyframes in DopeSheet, or things in the Viewport and I belive in you, you will adjust your Habits and you will handle that.
In a few weeks you will not go back.
You will G -> X ->5 and R -> Y ->90 and G-> Z -> 4 like a Pro!